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lfunc_lfunctions • Show schema
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{'Lhash': '2094248431233753335694201806217', 'a10': [-231.38263626694177, 0.0], 'a2': [-9.255305450677671, 0.0], 'a3': [9.0, 0.0], 'a4': [53.660678985343814, 0.0], 'a5': [25.0, 0.0], 'a6': [-83.29774905609904, 0.0], 'a7': [36.447817140087515, 0.0], 'a8': [-200.47620027843192, 0.0], 'a9': [81.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 26.46333026914181, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-9.0, 0]]], [5, [[1.0, 0], [-25.0, 0]]], [11, [[1.0, 0], [121.0, 0]]]], 'bad_primes': [3, 5, 11], 'central_character': '165.1', 'coefficient_field': 'CDF', 'conductor': 165, 'conductor_radical': 165, 'degree': 2, 'euler_factors': [[[1.0, 0], [9.255305450677671, 0], [32.0, 0]], [[1.0, 0], [-9.0, 0]], [[1.0, 0], [-25.0, 0]], [[1.0, 0], [-36.447817140087515, 0], [16807.0, 0]], [[1.0, 0], [121.0, 0]], [[1.0, 0], [878.0321319299917, 0], [371293.0, 0]], [[1.0, 0], [-155.3851317977659, 0], [1419857.0, 0]], [[1.0, 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['1.65207071322074254971014894368912', '2.69442915745644190984397759166985', '4.81813386704793197314484513085864', '6.60430373285099731449965007459813', '7.58765644839194753908363378023752', '8.446637262097494723882953486691322', '9.369676587058756600020413038646454', '10.11555758995383618390600633519000', '10.95234006513408669213722949421975'], 'prelabel': '2-165-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.144252158394047, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.65207071322074254971014894369', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.69442915745644190984397759167', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.81813386704793197314484513086', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 26.46333026914181, 'bad_primes': [3, 5, 11], 'central_character': '1.1', 'conductor': 165, 'conductor_radical': 165, 'degree': 2, 'index': 21, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/165/6/a/a/1/1'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '2-165-1.1-c5-0-21', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 1, 'prelabel': '2-165-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.144252158394047, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '1.65207071322074254971014894369', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2094248431233753335694201806217', 'Lhash_array': ['2094248431233753335694201806217'], 'label': '2-165-1.1-c5-0-21', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/165/6/a/a/1/1'}